AMH2 Integrable Systems
General Information
This page relates to the Applied Mathematics Honours course "Integrable Systems".
Lecturer(s) for this course: Nalini Joshi and Milena Radnovic.
For general information on honours in the School of Mathematics and Statistics, refer to the relevant honours handbook.
Exam
The exam paper will be available via Blackboard on Friday 10 June at 11 am. The solutions are due on Monday 13 June at 1pm and should be submitted via TurnItIn and emailed to the lecturers.Course outline
Integrable Systems
An Honours Course in Applied Mathematics
Nalini Joshi and Milena Radnović
Weekly questions will be given below as PDF files.
Lectures delivered in the AGR will be placed here as PDF files.
The mathematical theory of integrable systems has been described as one of the most profound advances of twentieth century mathematics. They lie at the boundary of mathematics and physics and were discovered through a famous paradox that arises in a model devised to describe the thermal properties of metals (called the FermiPastaUlam paradox).
In attempting to resolve this paradox, Kruskal and Zabusky discovered exceptional properties in the solutions of a nonlinear PDE, called the Kortewegde Vries equation (KdV). These properties showed that although the solutions are waves, they interact with each other as though they were particles, i.e., without losing their shape or speed, until then thought to be impossible for solutions of nonlinear PDEs. Kruskal invented the name solitons for these solutions. Here is a picture of two solitons interacting.
Solitons are known to arise in other nonlinear PDEs and also in partial difference equations. These systems and their symmetry reductions are now called integrable systems. These systems occur as universal limiting models in many physical situations.
This course introduces the mathematical properties of such systems. In particular, we will study their solutions, symmetry reductions called the Painlevé equations and their discrete versions. It focuses on mathematical methods created to describe the solutions of such equations and their interrelationships. More details about the course, including course objectives and outcomes and details about the assessment and exam can be read on the Information Sheet (PDF).
 References:
 M. J. Ablowitz and H. Segur, Solitons and the inverse scattering transform, SIAM, Philadelphia, USA, 1981.
 M. J. Ablowitz and P.A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering, Cambridge University Press, Cambridge, UK, 1991.
 P.G. Drazin and R.S. Johnson, Solitons: an introduction, Cambridge University Press, Cambridge, UK, 1989.
 M. Noumi, Painlevé equations through symmetry, American Mathematical Society, Providence, R.I., USA, 2004.
 Interesting Links on Solitons:
 An account of John Scott Russell's discovery of "that singular and beautiful phenomenon, which I have called the wave of translation."
 A modern attempt by mathematicians to recreate Scott Russell's wave in the Union Canal near Edinburgh.
 The Wikipedia page on Solitons (whose first and second definitions are still not correct).
 The Wikipedia page on the Kortewegde Vries equation.
Last modified: 20 February 2016 by n.joshi
Online resources
Monday lecture notes  Wednesday lecture notes  Assignments  

Week 1  Lecture 1  Lecture 2  Assignment 1 / Solution 
Week 2  Lecture 3  Lecture 4  Assignment 2 / Solution 
Week 3  Lecture 5  Lecture 6  Assignment 3 / Solution 
Week 4  Lecture 7  Lecture 8  Assignment 4 / Solution 
Semester break  
Week 5  Lecture 9  Lecture 10  Assignment 5 / Solution 
Week 6  Lecture 11  Lecture 12  Assignment 6 / Solution 
Week 7  Lecture 13  Lecture 14  Assignment 7 / Solution 
Week 8  Anzac Day  Lecture 15  Assignment 8 / Solution 
Week 9  Lecture 16  Lecture 17  Assignment 9 / Solution 
Week 10  Lecture 18  Lecture 19  
Week 11  Lecture 20  Lecture 21  Assignment 10 / Solution 
Week 12  Lecture 22  Lecture 23 
Timetable
Last revised 31/05/16
AMH2  Monday  Tuesday  Wednesday  Thursday  Friday 

10am 
Lecture AGR (Wks 17,912) N.Joshi M.Radnovic 




2pm 


Lecture AGR (Wks 112) N.Joshi M.Radnovic 

